Download 4/7 10.1-10.3 Quiz Review answers File

Name:
Date:
Geometry
10.1-10.3 Quiz Review
10.1 Tangents to Circles
1. chord 2. secant 3. radius
5. tangent 6. radius 7. chord
What is a tangent line?
4. diameter
8. radius
A line that touches the circle at exactly one point.
How can you tell if a common tangent is internal or external?
Internal: cuts through the segment connecting the two centers of the circles.
External: doesn’t.
9. Draw in a common internal tangent and a common external tangent. Label which is which.
external
internal
10. Tell whether line AB is tangent to circle
C. Explain your reasoning.
Yes; 72 + 242 = 252, so by Pythagorean Thm.
Converse, ΔABC is a right triangle and the
radius CA is perpendicular to BA. So BA must
be a tangent.
11. Lines AB and AD are tangent to circle C.
Find the value of x. Explain your
reasoning.
Tangent segments (BA
and DA) from the same exterior point (A) are
congruent, so 2x + 8 = 4x. x = 4.
Name:
Date:
Geometry
10.2 Arcs and Chords
1.
a) 110º
b) 200º
c) 160º
d) 250º
2. Use the given information to find the value of x. Explain which theorems you needed to use.
x
Since chords AB and DE are both 10, they are equidistant from the center. So CF = CG = x.
Since CG is perpendicular to DE and is a diameter (if you extend it), it must also bisect DE.
So DE = GE = 5.
Then by the Pythagorean theorem, x2 + 52 = 62, so x = √11.
10.3 Inscribed Angles
Explain how to find the center of a circle using two chords.
Draw two chords. Find the perpendicular bisector of each chord. Each must be a diameter. Their
intersection must be the center.
How do you find the measure of an inscribed angle?
Measure of inscribed angle = ½ measure of intercepted arc
OR measure of intercepted arc = 2*measure of inscribed angle
What do you know about an inscribed triangle? an inscribed quadrilateral?
If one side of the triangle is a diameter, then the angle opposite it is a right angle (i.e., that diameter is
the hypotenuse).
A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary.
Find the value of each variable.
1.
3.
Inscribed angle = ½ intercepted arc
These angles are inscribed angles sharing the
same intercepted arc, so they are congruent.
3x = ½ 138
80 = 3x + 5
3x = 69
75 = 3x
x = 23
25 = x
2.
4.
Inscribed quad. has opposite angles
supplementary.
Since the inscribed angle is right, the segment
is a diameter. So the arc is a semicircle.
2x + x + 12 = 180º
4x + 8 = 180º
3x = 168
4x = 172
x = 56
x = 43
4y + 5y = 180º
9y = 180
y = 20